FIGURE $620$

$6\mathrm{.}7.$ Iigure $6\mathrm{.}20$ show's the one$-$line diagram of a simple three$-$bus power system will gencration al bus $1.$ The vollage at bus $1$ is $V_1=\frac{1\mathrm{.}0}{{?}_U}$ pre unil The scheduled loads on buses $2$ and $3$ are marked on the diagram. Line impedances are marked in per unit on a IOI MVA hase. For the purpose of hand calculations, line resistances and line charging susceptances are neslecterl.

a$)$ Find the bus admittance matrix of the system.

b$)$ Find the voltage $($magnitude and phase$)$ of bus $2$ and $3$ using Gauss$-$Seidel method: $1)$ by hand $($at least $2$ iterations$),$ and, $2)$ by MATLAB $(10$ iterations$).$

c$)$ Using the values in part $($b$),$ find the current in each line and the complex power at bus $1.$

d$)$ Simulate the system in Power World Simulator and show all the values of parts $($b$)$ and $($c$)$ on the simulation $($see instructions ne